Choose an application
Choose an application
Choose an application
Choose an application
Focusing on the role that automorphisms and equivalence relations play in the algebraic theory of minimal sets provides an original treatment of some key aspects of abstract topological dynamics. Such an approach is presented in this lucid and self-contained book, leading to simpler proofs of classical results, as well as providing motivation for further study. Minimal flows on compact Hausdorff spaces are studied as icers on the universal minimal flow M. The group of the icer representing a minimal flow is defined as a subgroup of the automorphism group G of M, and icers are constructed explicitly as relative products using subgroups of G. Many classical results are then obtained by examining the structure of the icers on M, including a proof of the Furstenberg structure theorem for distal extensions. This book is designed as both a guide for graduate students, and a source of interesting new ideas for researchers.
Topological dynamics. --- Algebraic topology. --- Automorphisms.
Choose an application
Topological dynamics. --- Stability. --- Differential equations.
Choose an application
Choose an application
Topological dynamics. --- Dynamics, Topological --- Differentiable dynamical systems
Choose an application
Systèmes dynamiques --- Mathematiques --- Topological dynamics --- Colloque
Choose an application
"We study dynamics of the horocycle flow on strata of translation surfaces, introduce new invariants for ergodic measures, and analyze the interaction of the horocycle flow and real Rel surgeries. We use this analysis to complete and extend results of Calta and Wortman classifying horocycle-invariant measures in the eigenform loci. In addition we classify the horocycle orbit-closures and prove that every orbit is equidistributed in its orbit-closure. We also prove equidistribution results describing limits of sequences of measures. Our results have applications to the problem of counting closed trajectories on translation surfaces of genus 2"--
Topological dynamics. --- Ergodic theory. --- Random dynamical systems.
Choose an application
Potential theory (Mathematics) --- Topological dynamics --- Topological spaces